Question

A researcher wanted to test the claim that members of college sororities have grade point averages (GPA) above the mean GPA of 2.64 for all college students. She collected a random sample of 50 members of college sororities that had a mean GPA of 2.82. It is known that the population standard deviation for GPA is 0.90. Conduct a hypothesis test for this situation at the 0.05 level of significance and indicate what the researcher should conclude.

Answer 1

Solution :

Given that,

Population mean = = 2.64

Sample mean = = 2.82

Population standard deviation = = 0.90

Sample size = n = 50

Level of significance = = 0.05

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 2.64

Ha: 2.64

The test statistics,

Z =( - )/ (/n)

= ( 2.82 - 2.64 ) / ( 0.90 / 50)

= 1.414

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.96

Since it is observed that z = 1.414 < 0.05, it is then concluded that the null hypothesis is fails to reject.

P- Value = 1 - P(Z < z )

= 1 - P( Z < 1.41)

= 1 - 0.9207

= 0.0787

The p-value is p = 0.0787 , and since p = 0.0787 > 0.05, it is concluded that the null hypothesis is fails to reject.

Conclusion :

It is concluded that the null hypothesis Ho is fails to reject. Therefore, there is not enough evidence to claim that members of college sororities have grade point averages (GPA) above the mean GPA of 2.64 for all college students at 0.05 level of significance.